The study of electronic properties of graphene, as well as other semimetals, is an example of such challenges. Graphene quasiparticles are massless[1]}, [2]}, so graphene physics becomes extremely non-local. A large effective coupling constant (with the electric field) makes it also a strongly interacting theory. Thus, the physics of electronic excitations of electron states in graphene is an important area where the Monte Carlo methods are applied.
